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Analysis of Heavy Metal Pollution in Urban Topsoil

With the rapid development of urban economy and the continuous increase of urban population, the impact of human activities on urban environmental quality has become increasingly prominent. The verification of urban soil geological environment anomalies, and how to use the massive data obtained from the verification to carry out urban environmental quality evaluation and study the evolution mode of urban geological environment under the influence of human activities have increasingly become the focus of attention.

According to the functional division, urban areas can generally be divided into living areas, industrial areas, mountainous areas, main roads and parks, and divided into 1 area, 2 areas, ... and 5 areas. Different regional environments are affected by human activities to different degrees.

The soil geological environment of a city was investigated. Therefore, the investigated urban area is divided into grid areas with the spacing of about 1 km, and the surface soil (0 ~ 1 0 cm depth) is sampled and numbered according to each square kilometer1sampling point, and the positions of sampling points are recorded by GPS. The concentration data of various chemical elements contained in each sample are obtained by testing and analyzing with special instruments. On the other hand, samples are taken from natural areas 2 kilometers away from people and industrial activities as background values of elements in urban topsoil.

Attachment 1 lists the location, altitude and functional area of the sampling point, attachment 2 lists the concentrations of eight major heavy metal elements at the sampling point, and attachment 3 lists the background values of eight major heavy metal elements.

Now you are required to complete the following tasks through mathematical modeling:

(1) The spatial distribution of eight main heavy metal elements in urban areas is given, and the pollution degree of heavy metals in different areas of urban areas is analyzed.

(2) Through data analysis, the main reasons of heavy metal pollution were explained.

(3) Analyze the propagation characteristics of heavy metal pollutants and establish a model to determine the location of pollution sources.

(4) Analyze the advantages and disadvantages of your model, and what information should be collected in order to better study the evolution model of urban geological environment? With this information, how to build a model to solve the problem?

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Question B: Setting and Scheduling of Traffic Patrol Service Platform

"Call the police when you are in trouble" is a well-known buzzword. The police shoulder four functions: criminal law enforcement, public security management, traffic management and serving the masses. In order to realize these functions more effectively, it is necessary to set up traffic patrol service platforms in some traffic arteries and important parts of the city. The functions and police force of each traffic patrol service platform are basically the same. Due to the limited police resources, how to reasonably set up the traffic patrol service platform, allocate the jurisdiction of each platform and dispatch police resources according to the actual situation and needs of the city is a realistic topic faced by the public security department.

Try to establish a traffic patrol service platform in a city, and establish a mathematical model to analyze and study the following problems:

(1) The attached figure 1 in annex 1 gives a schematic diagram of the traffic network in downtown A and the existing 20 traffic patrol service platforms. See Annex 2 for relevant data and information. Please assign jurisdiction to each traffic patrol service platform, so that a traffic patrol (with a police car speed of 60km/h) can arrive at the incident site within 3 minutes as far as possible when an emergency occurs within the jurisdiction.

For major emergencies, it is necessary to dispatch the police resources of 20 traffic patrol service platforms in the whole region to achieve a rapid and comprehensive blockade of the access area 13 traffic arteries. In fact, the police force on a platform blocks at most one intersection. Please give a reasonable scheduling scheme for the police force of the traffic patrol service platform in this area.

In view of the unbalanced workload of the existing traffic patrol service platform and the long police time in some places, it is planned to add 2 to 5 more platforms in this regard. Please confirm the specific number and location of platforms to be added.

(2) According to the specific situation of the whole city (six districts of A, B, C, D, E and F in the main city), according to the principles and tasks of setting up the traffic patrol service platform, analyze and study the rationality of the existing traffic patrol service platform in this city (see Annex). If it is obviously unreasonable, please give a solution.

If a major criminal case occurs in the city's location P (node P(32), an alarm is received 3 minutes after the incident, and the suspect has fled by car. In order to quickly search for suspects, please give the best containment scheme for dispatching police resources on the municipal traffic patrol service platform.

Attachment1:Schematic diagram of traffic network and platform setting in Area A and City Six.

Attachment 2: Data sheets related to traffic network and platform setting in the sixth district of the city (***5 worksheets).

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C. Reform of the pension system for retired employees in enterprises

Pension, also known as pension, is an insurance treatment paid in the form of money according to workers' contribution to society and their eligibility for endowment insurance, which is used to protect the basic needs of employees after retirement.

The basic old-age insurance for enterprise employees in China adopts the mode of "social pooling" and "personal account", that is, the enterprise pays the total wages of employees to the social pooling fund account according to a certain proportion (20%), and then pays the personal wages of employees to the personal account according to a certain proportion (8%). These two accounts are collectively referred to as the endowment insurance fund. After retirement, according to the ratio of the employee's monthly (or annual) payment wage to the average social wage (payment index), considering the factors such as the average social wage in the year before retirement, the funds (basic pension) are allocated from the social pooling account, and a certain proportion of the funds in the personal wage account (personal account pension) are used as the monthly pension after retirement. The pension will be adjusted with the adjustment of the average social wage. When an employee dies, the funds in the social pooling account will not be returned to the employee, and the balance in the personal account can be inherited. Personal account deposits bear interest according to the one-year deposit rate announced by the bank at that time. For simplicity, the interest rate is set at 3%.

The payment of pension is closely related to the wages of employees and the average social wage; The increase in wages is related to economic growth. In the past 30 years, China's economy has developed rapidly, and the wage growth rate is also very high. However, the economic and wage growth rates in developed countries are low. The strategic goal of China's economic development is to make China's per capita GNP reach the level of moderately developed countries in the middle of 2 1 century.

At present, the old-age insurance reform in China is in a transitional period. An important goal of endowment insurance management is to balance the income and expenditure of endowment insurance fund, which is related to social stability and the smooth transition of an aging society. An important factor affecting the balance of income and expenditure of endowment insurance fund is the substitution rate. The replacement rate refers to the proportion of pension when employees just retire to their pre-retirement wages. According to the general thinking of the country on the basic old-age insurance system, the target replacement rate of the basic old-age insurance in the future is determined to be 58.5%. The replacement rate is low, the living standard of retired workers is low, and the balance of income and expenditure of endowment insurance fund is easy to maintain. If the replacement rate is high, the living standard of retired workers will be high, and the balance of pension funds will be difficult to maintain, and there may be a gap. The so-called gap refers to the balance of payments when the endowment insurance fund cannot make ends meet.

Attachment 1 is the average wage data of employees in Shandong province over the years; Annex 2 is the salary distribution of employees in an enterprise in Shandong Province in 2009, and Annex 3 is the calculation method of pension. Please establish a mathematical model to solve the following problems:

Question 1: Make what you think is a simplified and reasonable assumption about the future situation of China's economic development and wage growth. Please refer to Annex 1 Forecast 20 1 1 Average annual wage of employees in Shandong Province by 2035.

Question 2: According to Annex 2, calculate the proportion of wages of employees of all ages in this enterprise to the average wage of this enterprise in 2009. If these proportions are taken as the reference value of the employee contribution index, consider that the employees of this enterprise began to pay pension insurance at the age of 30 and 40 respectively from 2000 to retirement (55, 60 and 65), and calculate the pension replacement rate under various circumstances.

Question 3: Suppose an employee of this enterprise began to pay endowment insurance at the age of 30 in 2000 until retirement (55, 60, 65), and began to receive pension from retirement until his death at the age of 75. Calculate the gap of the endowment insurance fund and the age of the employee receiving the pension, and the balance between the pension fund he paid and the pension he received will be reached.

Question 4: What measures do you think can be taken to achieve the target replacement rate and maintain the balance of pension funds? Please give your reasons.

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D topic natural casing collocation problem

The production and processing of natural casing (hereinafter referred to as casing) is a traditional industry in China, and its export volume ranks first in the world. The cleaned casing is divided into small pieces (raw materials) with different lengths and enters the assembly process. The traditional production method relies on manpower, while measuring the length of raw materials and calculating in the mind, assembling raw materials into finished products (bundles) according to the specified quantity and total length.

Raw materials are graded according to length, usually 0.5m as a grade, for example, 3-3.4m is 3m, 3.5m-3.9m is 3m, and so on. Table 1 shows the specifications of several common finished products. The unit of length is meters. ∞ means there is no upper limit, but the actual length is less than 26 meters.

Table 1 finished product specification table

Minimum length, maximum length, number of elements and total length.

3 6.5 20 89

7 13.5 8 89

14 ∞ 5 89

In order to improve production efficiency, the company plans to change the assembly process, first measure all raw materials and establish a list of raw materials. Table 2 is a description of a batch of raw materials.

Table 2 Description of raw materials

Length 3-3.4 3.5-3.9 4-4.4 4.5-4.9 5-5.4 5-5.9 6-6.4 6.5-6.9

Root number 43 59 39 465 438+0 27 28 34 265 438+0

Length 7-7.4 7.5-7.9 8-8.4 8.5-8.9 9-9.4 9.5-9.910-10.410.5-10.9.

Root number 24 24 20 25 2123 2118

Length11-1.41.5-1.912-12.4/.

Root number 3 1 23 22 59 18 25 35 29

Length15-15.415.5-16-16.5-16.9 65438+.

Number of roots 30 42 28 42 45 49 50 64

Length19-19.419.5-19.9 20-20.4 20.5-20.9 21.421.5-2/kloc-.

Number of roots 52 63 49 35 27 65 438+06 65 438+02 2

Length 23-23.4 23.5-23.9 24-24.4 24.5-24.9 25-25.4 25.5-25.9

Root number 0 6000 1

According to the above description of finished products and raw materials, a raw material collocation scheme is designed, and workers can produce according to this scheme.

The company has the following specific requirements for the matching scheme:

(1) For a given batch of raw materials, the more bundles of finished products, the better;

(2) For the scheme with the same number of bundles of finished products, the more finished products with the shortest length, the better the scheme;

(3) In order to improve the utilization rate of raw materials, the total length is allowed to have an error of 0.5m, and the total number of roots is allowed to be less than the standard1;

(4) Raw materials corresponding to a certain specification, if surplus, can be degraded and used. For example, raw materials with a length of 14m can be bundled with those with a length of 7- 13.5m, and the finished product belongs to the specification of 7- 13.5m;

(5) In order to keep the food fresh, it is required to come up with a plan within 30 minutes.

Please establish the mathematical model of the above problems, give the solution, and solve the actual data given in table 1 and table 2, and give the collocation scheme.